Iterative Solutions of the Equations Jor Plane Oblique Shock Waves

1959 ◽  
Vol 63 (587) ◽  
pp. 669-672 ◽  
Author(s):  
A. R. Collar
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Free Stream ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Two Dimensional ◽  
Iterative Solutions ◽  
Flow Through ◽  
Image Position

If a plane oblique shock wave, inclined to the free stream at the angle ε, is produced in two-dimensional supersonic flow of Mach number M by (for example) a wedge which deflects the flow through an angle δ, the equation connecting these quantities may be writtenIn this form, δ is given explicitly when M, ε are fixed. Similarly, we may obtain M explicitly when ε, δ are fixed; equation (1) may be written (see, for example, Liepmann and Puckett, Equation 4.27)

Experimental Research of Gasdynamic Liquid Drops Breakup in the Supersonic Flow with an Oblique Shock Wave

2020 ◽  
Author(s):  
K. Yu. Arefyev ◽  
O. V. Guskov ◽  
A. N. Prokhorov ◽  
A. S. Saveliev ◽  
E. E. Son ◽  
...  
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Experimental Research ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Liquid Drops

scholarly journals Instabilities in oblique shock wave/laminar boundary-layer interactions

2016 ◽  
Vol 789 ◽  
pp. 1-35 ◽  
Author(s):  
F. Guiho ◽  
F. Alizard ◽  
J.-Ch. Robinet
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Shear Layer ◽  
Laminar Boundary Layer ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Two Dimensional ◽  
Linear Framework ◽  
Displacement Thickness ◽  
The Impact

The interaction of an oblique shock wave and a laminar boundary layer developing over a flat plate is investigated by means of numerical simulation and global linear-stability analysis. Under the selected flow conditions (free-stream Mach numbers, Reynolds numbers and shock-wave angles), the incoming boundary layer undergoes separation due to the adverse pressure gradient. For a wide range of flow parameters, the oblique shock wave/boundary-layer interaction (OSWBLI) is seen to be globally stable. We show that the onset of two-dimensional large-scale structures is generated by selective noise amplification that is described for each frequency, in a linear framework, by wave-packet trains composed of several global modes. A detailed analysis of both the eigenspectrum and eigenfunctions gives some insight into the relationship between spatial scales (shape and localization) and frequencies. In particular, OSWBLI exhibits a universal behaviour. The lowest frequencies correspond to structures mainly located near the separated shock that emit radiation in the form of Mach waves and are scaled by the interaction length. The medium frequencies are associated with structures mainly localized in the shear layer and are scaled by the displacement thickness at the impact. The linear process by which OSWBLI selects frequencies is analysed by means of the global resolvent. It shows that unsteadiness are mainly associated with instabilities arising from the shear layer. For the lower frequency range, there is no particular selectivity in a linear framework. Two-dimensional numerical simulations show that the linear behaviour is modified for moderate forcing amplitudes by nonlinear mechanisms leading to a significant amplification of low frequencies. Finally, based on the present results, we draw some hypotheses concerning the onset of unsteadiness observed in shock wave/turbulent boundary-layer interactions.

Effects of plasma aerodynamic actuation on oblique shock wave in a cold supersonic flow

2009 ◽  
Vol 42 (16) ◽  
pp. 165503 ◽  
Author(s):  
Jian Wang ◽  
Yinghong Li ◽  
Bangqin Cheng ◽  
Changbing Su ◽  
Huimin Song ◽  
...  
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Oblique Shock ◽  
Oblique Shock Wave

Interaction of oblique shock waves and planar mixing regions

1996 ◽  
Vol 306 ◽  
pp. 43-57 ◽  
Author(s):  
D. R. Buttsworth
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Wave Equations ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Density Gradients ◽  
Similar Treatment ◽  
Specific Heats ◽  
Shock Oscillation ◽  
Nonuniform Gas

An analysis for predicting the interaction of a steady oblique shock wave and a planar mixing region is presented. Specifically, an equation for the shock curvature was obtained from the shock wave and isentropic wave difference equations which govern the shock transmission within a region of varying Mach number. The effects of nonuniform gas composition within the mixing region were assessed using a similar treatment; however, the wave equations were expanded in terms of a varying ratio of specific heats instead of a varying Mach number. An expression for the shock-induced vorticity due to velocity and density gradients within the mixing region was also obtained. This expression provides a means of estimating the possible mixing augmentation induced in various shock wave-mixing region interactions. When the velocity and density gradients within the mixing region oppose each other, it is demonstrated that the pre-shock vorticity may be attenuated by the shock. Applications of the analysis are discussed with reference to specific examples involving mixing augmentation and shock oscillation.

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